What Biden has done is to cut the issuance of drilling leases to the minimum required by law, pass the Inflation Reduction Act, enact a regulation to force vehicle electrification, and similarly force fossil fuels out of most power plants.
What Biden has not done: stop issuing drilling permits or impose export restrictions on fossil fuels. The former has some serious limits because of how the courts treat the right to drill as a property right once you hold a drilling lease, and the latter is simply untested.
Union growth was at its strongest in American history during the period between 1900-1920. There were already millions of union members decades before FDR ever took office. It was a 50+ year battle starting in the 1800s, I don’t think I’d call that starting. I’d call FDR the results of that movement, if anything.